When a human being exhales CO₂, what is, by the numbers, the main source of carbon atoms exiting the body in this way? I mean what class of cells, or which tissues are the biggest on a pie chart of where carbon atoms breathed out in the form of CO₂ molecules came from?

Duh, I just realized it's probably mostly from leftovers after the sugars that you eat are burned for energy. I've also heard that broken-down fat from weight-losers gets breathed out. Is that at all true?
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PeteDec 4 '12 at 18:51

yes, the CO2 is the product of various metabolic processes. I can expand if you want...
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MattDMoDec 4 '12 at 19:28

3 Answers
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CO2 is a product of Cellular Respiration, which generally takes Glucose and molecular Oxygen to produce Carbon Dioxide, water, heat, and allows ADP to be regenerated into ATP (or other various oxidation reactions). The Carbon comes from wherever the acetyl-CoA used in the Citric Acid Cycle came from - either carboyhydrates or fatty-acids (saturated carbon chains).

So, you are correct. CO2 transferring out of the lungs is mostly the result of burning sugars (or fats) for energy (the regeneration of ADP/GDP with respect to human biology).

To that end, the tissues that produce the most CO2 will be the cell-types which constantly require energy. Nominally, muscle tissues.

Per your comment, broken down fat, or rather, the process of Fatty-Acid Catabolism, results in the production of acetyl-CoA, which is a primary player in the Citric-Acid Cycle. The Citric Acid Cycle, which you should recognize as the Cycle that Pyruvate - the end result of Glycolysis (the breakdown of Glucose into 2x 3-Carbon Pyruvates) - also goes into after being converted into acetyl-CoA by Pyruvate Dehydrogenase.

In the resting state it's the brain that is responsible for the largest proportion of cellular respiration: estimates vary but are usually in the 20-25% range. This is because even at rest the nervous system is working hard to maintain the ion gradients that are essential for propagation of action potentials.
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Alan BoydDec 4 '12 at 19:47

The original questions seems to me to be asking for information about which tissues or organs are responsible for producing most of the exhaled CO2. As other answers have mentioned, CO2 production by cells reflects the amount of oxidative metabolism that is being carried out. This means that we can answer the question by simply asking - which tissues/organs are responsible for consuming the most O2?

There are many sources of information about this, but the most succinct statement that I have found is here:

The average human body of 139 lb (63 kg) consumes 250 ml of O2 each minute. The major single-organ oxygen consumers are the liver, brain, and heart (consuming 20.4%, 18.4%, and 11.6%, respectively), while the sum total of all the body's skeletal muscles consume about 20%. In addition, the kidneys use up about 7.2%, and the skin uses 4.8%. The rest of the body consumes the remaining 17.6% of the oxygen. Oxygen use can also be measured per 100 gm of an organ to indicate concentrations of use; as such, heart usage is highest, followed by the kidneys, then the brain, and then the liver. During exercise, the biochemical oxygen demand increases for active tissues including the heart and skeletal muscles.

Other sources are in broad agreement with this. Note however that these are values at rest. As the quotation states, during active exercise the skeletal muscle will become the major source of CO2.